// Code extracted from ulmBLAS: https://github.com/michael-lehn/ulmBLAS-core

#ifndef GEMM_HPP
#define GEMM_HPP
#include <algorithm>
#include <cstdlib>

#if defined(_OPENMP)
#include <omp.h>
#endif

//-- new with alignment --------------------------------------------------------
void *
malloc_(std::size_t alignment, std::size_t size)
{
    alignment = std::max(alignment, alignof(void *));
    size     += alignment;

    void *ptr  = std::malloc(size);
    void *ptr2 = (void *)(((uintptr_t)ptr + alignment) & ~(alignment-1));
    void **vp  = (void**) ptr2 - 1;
    *vp        = ptr;
    return ptr2;
}

void
free_(void *ptr)
{
    std::free(*((void**)ptr-1));
}

//-- Config --------------------------------------------------------------------

#ifdef HAVE_FMA

#   ifndef BS_D_MR
#   define BS_D_MR 4
#   endif

#   ifndef BS_D_NR
#   define BS_D_NR 12
#   endif

#   ifndef BS_D_MC
#   define BS_D_MC 256
#   endif

#   ifndef BS_D_KC
#   define BS_D_KC 512
#   endif

#   ifndef BS_D_NC
#   define BS_D_NC 4092
#   endif

#   ifndef BS_D_ALIGN
#   define BS_D_ALIGN 32
#   endif

#endif


#ifndef BS_D_MR
#define BS_D_MR 4
#endif

#ifndef BS_D_NR
#define BS_D_NR 8
#endif

#ifndef BS_D_MC
#define BS_D_MC 256
#endif

#ifndef BS_D_KC
#define BS_D_KC 256
#endif

#ifndef BS_D_NC
#define BS_D_NC 4096
#endif

#ifndef BS_D_ALIGN
#define BS_D_ALIGN 32
#endif


template <typename T>
struct BlockSize
{
    static const int MC = 64;
    static const int KC = 64;
    static const int NC = 256;
    static const int MR = 8;
    static const int NR = 8;

    static const int align = alignof(T);

    static_assert(MC>0 && KC>0 && NC>0 && MR>0 && NR>0, "Invalid block size.");
    static_assert(MC % MR == 0, "MC must be a multiple of MR.");
    static_assert(NC % NR == 0, "NC must be a multiple of NR.");
};


template <>
struct BlockSize<double>
{
    static const int MC    = BS_D_MC;
    static const int KC    = BS_D_KC;
    static const int NC    = BS_D_NC;
    static const int MR    = BS_D_MR;
    static const int NR    = BS_D_NR;

    static const int align = BS_D_ALIGN;

    static_assert(MC>0 && KC>0 && NC>0 && MR>0 && NR>0, "Invalid block size.");
    static_assert(MC % MR == 0, "MC must be a multiple of MR.");
    static_assert(NC % NR == 0, "NC must be a multiple of NR.");
};

//-- aux routines --------------------------------------------------------------
template <typename Alpha, typename MX, typename MY>
void
geaxpy(const Alpha &alpha, const MX &X, MY &Y)
{
    assert(X.size1()==Y.size1());
    assert(X.size2()==Y.size2());

    typedef typename MX::size_type  size_type;

    for (size_type j=0; j<X.size2(); ++j) {
        for (size_type i=0; i<X.size1(); ++i) {
            Y(i,j) += alpha*X(i,j);
        }
    }
}

template <typename Alpha, typename MX>
void
gescal(const Alpha &alpha, MX &X)
{
    typedef typename MX::size_type  size_type;

    for (size_type j=0; j<X.size2(); ++j) {
        for (size_type i=0; i<X.size1(); ++i) {
            X(i,j) *= alpha;
        }
    }
}

template <typename Index, typename Alpha, typename TX, typename TY>
void
geaxpy(Index m, Index n,
       const Alpha &alpha,
       const TX *X, Index incRowX, Index incColX,
       TY       *Y, Index incRowY, Index incColY)
{
    for (Index j=0; j<n; ++j) {
        for (Index i=0; i<m; ++i) {
            Y[i*incRowY+j*incColY] += alpha*X[i*incRowX+j*incColX];
        }
    }
}

template <typename Index, typename Alpha, typename TX>
void
gescal(Index m, Index n,
       const Alpha &alpha,
       TX *X, Index incRowX, Index incColX)
{
    if (alpha!=Alpha(0)) {
        for (Index j=0; j<n; ++j) {
            for (Index i=0; i<m; ++i) {
                X[i*incRowX+j*incColX] *= alpha;
            }
        }
    } else {
        for (Index j=0; j<n; ++j) {
            for (Index i=0; i<m; ++i) {
                X[i*incRowX+j*incColX] = Alpha(0);
            }
        }
    }
}

//-- Micro Kernel --------------------------------------------------------------
template <typename Index, typename T>
void
ugemm(Index kc, T alpha,
      const T *A, const T *B,
      T beta,
      T *C, Index incRowC, Index incColC)
{
    const Index MR = BlockSize<T>::MR;
    const Index NR = BlockSize<T>::NR;
    T P[BlockSize<T>::MR*BlockSize<T>::NR];

    for (Index l=0; l<MR*NR; ++l) {
        P[l] = 0;
    }
    for (Index l=0; l<kc; ++l) {
        for (Index j=0; j<NR; ++j) {
            for (Index i=0; i<MR; ++i) {
                P[i+j*MR] += A[i+l*MR]*B[l*NR+j];
            }
        }
    }
    for (Index j=0; j<NR; ++j) {
        for (Index i=0; i<MR; ++i) {
            C[i*incRowC+j*incColC] *= beta;
            C[i*incRowC+j*incColC] += alpha*P[i+j*MR];
        }
    }
}

#ifdef HAVE_AVX
#include "avx.hpp"
#endif

#ifdef HAVE_FMA
#include "fma.hpp"
#endif

//-- Macro Kernel --------------------------------------------------------------
template <typename Index, typename T, typename Beta, typename TC>
void
mgemm(Index mc, Index nc, Index kc,
      T alpha,
      const T *A, const T *B,
      Beta beta,
      TC *C, Index incRowC, Index incColC)
{
    const Index MR = BlockSize<T>::MR;
    const Index NR = BlockSize<T>::NR;
    const Index mp  = (mc+MR-1) / MR;
    const Index np  = (nc+NR-1) / NR;
    const Index mr_ = mc % MR;
    const Index nr_ = nc % NR;

    #if defined(_OPENMP)
    #pragma omp parallel for
    #endif
    for (Index j=0; j<np; ++j) {
        const Index nr = (j!=np-1 || nr_==0) ? NR : nr_;
        T C_[MR*NR];

        for (Index i=0; i<mp; ++i) {
            const Index mr = (i!=mp-1 || mr_==0) ? MR : mr_;

            if (mr==MR && nr==NR) {
                ugemm(kc, alpha,
                      &A[i*kc*MR], &B[j*kc*NR],
                      beta,
                      &C[i*MR*incRowC+j*NR*incColC],
                      incRowC, incColC);
            } else {
                ugemm(kc, alpha,
                      &A[i*kc*MR], &B[j*kc*NR],
                      T(0),
                      C_, Index(1), MR);
                gescal(mr, nr, beta,
                       &C[i*MR*incRowC+j*NR*incColC],
                       incRowC, incColC);
                geaxpy(mr, nr, T(1), C_, Index(1), MR,
                       &C[i*MR*incRowC+j*NR*incColC],
                       incRowC, incColC);
            }
        }
    }
}

//-- Packing blocks ------------------------------------------------------------
template <typename MA, typename T>
void
pack_A(const MA &A, T *p)
{
    typedef typename MA::size_type  size_type;

    size_type mc = A.size1();
    size_type kc = A.size2();
    size_type MR = BlockSize<T>::MR;
    size_type mp = (mc+MR-1) / MR;

    for (size_type j=0; j<kc; ++j) {
        for (size_type l=0; l<mp; ++l) {
            for (size_type i0=0; i0<MR; ++i0) {
                size_type i  = l*MR + i0;
                size_type nu = l*MR*kc + j*MR + i0;
                p[nu]        = (i<mc) ? A(i,j) : T(0);
            }
        }
    }
}

template <typename MB, typename T>
void
pack_B(const MB &B, T *p)
{
    typedef typename MB::size_type  size_type;

    size_type kc = B.size1();
    size_type nc = B.size2();
    size_type NR = BlockSize<T>::NR;
    size_type np = (nc+NR-1) / NR;

    for (size_type l=0; l<np; ++l) {
        for (size_type j0=0; j0<NR; ++j0) {
            for (size_type i=0; i<kc; ++i) {
                size_type j  = l*NR+j0;
                size_type nu = l*NR*kc + i*NR + j0;
                p[nu]        = (j<nc) ? B(i,j) : T(0);
            }
        }
    }
}

//-- Frame routine -------------------------------------------------------------
template <typename Alpha, typename MatrixA, typename MatrixB,
         typename Beta, typename MatrixC>
void
gemm(Alpha alpha, const MatrixA &A, const MatrixB &B, Beta beta, MatrixC &C)
{
    assert(A.size2()==B.size1());
    namespace ublas = boost::numeric::ublas;

    typedef typename MatrixC::size_type  size_type;
    typedef typename MatrixA::value_type TA;
    typedef typename MatrixB::value_type TB;
    typedef typename MatrixC::value_type TC;
    typedef typename std::common_type<Alpha, TA, TB>::type  T;

    const size_type MC = BlockSize<T>::MC;
    const size_type NC = BlockSize<T>::NC;
    const size_type MR = BlockSize<T>::MR;
    const size_type NR = BlockSize<T>::NR;

    const size_type m = C.size1();
    const size_type n = C.size2();
    const size_type k = A.size2();

    const size_type KC = BlockSize<T>::KC;
    const size_type mb = (m+MC-1) / MC;
    const size_type nb = (n+NC-1) / NC;
    const size_type kb = (k+KC-1) / KC;
    const size_type mc_ = m % MC;
    const size_type nc_ = n % NC;
    const size_type kc_ = k % KC;


    TC *C_ = &C(0,0);
    const size_type incRowC = &C(1,0) - &C(0,0);
    const size_type incColC = &C(0,1) - &C(0,0);

    T *A_ = (T*) malloc_(BlockSize<T>::align, sizeof(T)*(MC*KC+MR));
    T *B_ = (T*) malloc_(BlockSize<T>::align, sizeof(T)*(KC*NC+NR));

    if (alpha==Alpha(0) || k==0) {
        gescal(beta, C);
        return;
    }

    for (size_type j=0; j<nb; ++j) {
        size_type nc = (j!=nb-1 || nc_==0) ? NC : nc_;

        for (size_type l=0; l<kb; ++l) {
            size_type kc = (l!=kb-1 || kc_==0) ? KC : kc_;
            Beta beta_   = (l==0) ? beta : Beta(1);

            const auto Bs = subrange(B, l*KC, l*KC+kc, j*NC, j*NC+nc);
            pack_B(Bs, B_);

            for (size_type i=0; i<mb; ++i) {
                size_type mc = (i!=mb-1 || mc_==0) ? MC : mc_;

                const auto As = subrange(A, i*MC, i*MC+mc, l*KC, l*KC+kc);
                pack_A(As, A_);

                mgemm(mc, nc, kc,
                      T(alpha), A_, B_, beta_,
                      &C_[i*MC*incRowC+j*NC*incColC],
                      incRowC, incColC);
            }
        }
    }
    free_(A_);
    free_(B_);
}

#endif